The Ikea story has many of the ingredients of an epic saga. Ingvar Kamprad founded Sweden's furniture giant in 1943, but now – aged 86 – it is time for him to hand over control to his three sons. That raises questions about Ikea's sustainability, and his legacy.

At Helsingborg, the site of Ikea's Swedish headquarters, the sustainability manager, Jeanette Skjelmose, lavishes praise on Kamprad, underlining his intimate understanding of the firm. "We see him here quite often," she says. But these days, his role in the company is mostly advisory.

The communication manager, Ylva Magnusson, says: "He is no longer at the wheel." She wants to make it clear that he is no longer indispensable to the smooth running of the business. In January, the firm reported profits of $4.1bn for 2012, up 8% in this post-Kamprad era.

Kamprad has sometimes been Ikea's worst enemy, but he was also its essence. Behind the scenes, the management has to manage this paradox, using his image wisely, playing down his presence while retaining his flair.

"There is every reason to wonder what will happen when Kamprad is no longer there," says Susanne Sweet, a specialist in corporate social responsibility at the Stockholm School of Economics. "The image that has been built up around him – hard-working, parsimonious and close to ordinary people – does not work for his sons, who grew up in a completely different world. Do those values count for them?"

A photograph from 1998 illustrates the difficult succession. It was taken at Kamprad's traditional Christmas talk to staff at the Älmhult store. It was the first time one of his sons had addressed the assembly. The picture shows the old man looking worried, staring at his eldest son, Peter, as he gives his talk. Peter looks scared stiff. Was he really going to take over running the company, with its workforce of 150,000? Would he and his brothers be up to it? Kamprad has done nothing to make it easy for them.

The regional daily, Smålandsposten, published the photograph in August 2002 under the headline "Kamprad's three sons take over Ikea", with a piece by Bosse Vikingson, who had been following the company's fortunes for the previous 15 years. At the time it looked as though the order of succession had finally been settled. The eldest son Peter, then 38, was to take over from his father, the article explained, heading the Netherlands-based Stichting Ingka Foundation that controls the flat-pack chain. The two younger brothers were also to play their part, Jonas focusing on design, Mathias on business development.

But it was not that simple. None of the brothers enjoyed the omniscient powers invested in their father, who feared rivalry among the siblings. Every effort had been made to organise the empire so that it could not be broken up following a rift between the heirs. So what has happened since? Kamprad made one of his most recent public appearances last autumn, when the Älmhult store reopened after a refurbishment. Pictures show the old boss shaking hands and smiling, but firmly taken in hand by a swarm of minders. "He's old now," Vikingson points out. "Ikea's management is trying to make sure he doesn't do too much, even if they have no real control over him."

Last Christmas Kamprad was back on stage. Peter has not addressed an audience since the 1998 gathering at Älmhult. The brothers' rare appearances are carefully stage-managed. There has only been one interview, for a book vetted by Kamprad.

For the past three-and-a-half years, a Norwegian, Per Heggenes, has acted as the spokesman for Kamprad and sons. He explained that the brothers have given up any idea of operational responsibility in the Ikea organisation. Peter will not be taking over the reins. All three have made it clear they want to work as representatives of the shareholders in the various foundations. "But they don't just attend board meetings," Heggenes adds. "Their role is to ensure that the [Ikea] culture and philosophy are passed on to the next generation."

By a happy coincidence, their personalities seem suited to the task of protecting the three pillars on which the firm rests. Jonas, who is creative and a designer by training, is interested in product development. Mathias, the most enterprising, wants to concentrate on the overall concept. Peter, the economist, has done most to develop Ikano, the bank set up by his father.

"They would rather stay in the background," Heggenes says. "It gives them enough distance to supervise what is going on and uphold the core principles behind Ikea's success." Or as he said at another point, "Everything has been done to secure eternal life for Ikea."

This complicated set-up is meant to ensure Ikea survives the loss of its founder. Kamprad's spirit will surely continue to hang over the firm.

• This article appeared in Guardian Weekly, which incorporates material from Le Monde